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US6990092B1 - Iterative process for TDMA radiomobile communications - Google Patents

Iterative process for TDMA radiomobile communications Download PDF

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US6990092B1
US6990092B1 US09/585,352 US58535200A US6990092B1 US 6990092 B1 US6990092 B1 US 6990092B1 US 58535200 A US58535200 A US 58535200A US 6990092 B1 US6990092 B1 US 6990092B1
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channel
estimate
symbols
paths
timeslot
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Mohamed Siala
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Orange SA
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France Telecom SA
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/005—Control of transmission; Equalising
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0204—Channel estimation of multiple channels
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/24—Radio transmission systems, i.e. using radiation field for communication between two or more posts
    • H04B7/26—Radio transmission systems, i.e. using radiation field for communication between two or more posts at least one of which is mobile
    • H04B7/2643—Radio transmission systems, i.e. using radiation field for communication between two or more posts at least one of which is mobile using time-division multiple access [TDMA]

Definitions

  • the purpose of this invention is an iterative process for TDMA (Time Division Multiple Access) radiomobile communications.
  • TDMA Time Division Multiple Access
  • TDMA systems can be used to distribute several users communicating through the same radioelectric channel, in time [1, 3]. Each user is separated from the others by periodically assigning a timeslot to him in which he can transmit, and another timeslot in which he can receive. Protective intervals are allowed at each end of each timeslot in order to guard against imperfections in time synchronization between transmitters and interference between consecutive timeslots resulting from the plurality of pathways.
  • FIG. 1 attached thus shows timeslots TA 1 , TA 2 , . . . , TA N allocated to N users with protective intervals IG.
  • the radioelectric signal transmitted during a timeslot is obtained by transposition of the equivalent base band signal into frequency.
  • the base band signal is the result of filtering the data stream to be transmitted through a “transmission” filter.
  • the transmitted data stream is composed of two sequences of data symbols separated in time by a sequence of symbols known to the receiver, called the reference sequence.
  • the two sequences of data symbols may possibly originate from coding and interlacing of information to be transmitted.
  • the reference sequence frequently has good time correlation properties, in order to enable a precise estimate of the channel at the receiver.
  • CAZAC Constant Amplitude—Zero AutoCorrelation sequences [1, 4, 5] are sequences with components taken from the bipolar alphabet ⁇ 1, 1 ⁇ and possessing a null circular autocorrelation function everywhere except at the origin.
  • the radiomobile channel used during a communication between a transmitter and a receiver is usually of the multipath type with fast fading called RAYLEIGH fading.
  • the existence of several paths is due to the fact that the radioelectric wave is propagated along several paths between the transmission location and the reception location.
  • the received signal is then the sum of several more or less delayed replicas, more or less modified in phase and in amplitude.
  • the receiver applies filtering matched to the transmission filter and to the channel and it combines energy contributions from all transmitted signal replicas in an optimum manner.
  • the output signal from the matched filter is sampled at the rate of the symbols and it is whitened using a discrete filter called a whitener.
  • Samples at the output from the whitener filter supply a filtered and noisy version of the transmitted data stream.
  • the discrete filter associated with this filtered version also called the discrete channel, has a finite pulse response that varies from one sample to the other. It characterizes the production of the multipath channel during the corresponding reception timeslot, in an indirect manner.
  • Samples at the output from the whitener filter corresponding to the reference sequence are used to estimate the discrete channel [1, 4, 5]. This estimate of the discrete channel is used to equalize the remaining samples, so that the two transmitted data sequences can be detected if there are any.
  • the equalizer usually used is known as the VITERBI equalizer with flexible decisions [2]. As its name suggests, this equalizer uses an application of the Soft-Output Viterbi Algorithm (SOVA) [2] to produce soft decisions on all transmitted data symbols. These soft outputs are possibly de-interlaced and decoded to detect the information transmitted.
  • SOVA Soft-Output Viterbi Algorithm
  • FIG. 2 attached shows these transmission/reception operations.
  • the transmitter E comprises a data source 10 , an encoder/interlacer 12 outputting symbols a k , and a modulator 14 .
  • the multipath channel is symbolized by a block 20 .
  • the receiver R comprises a demodulator 30 (matched filter/whitener filter) outputting samples R k , a discrete channel estimator 32 , an equalizer 34 , a de-interlacer/decoder 36 and finally an addressee 38 .
  • a demodulator 30 matched filter/whitener filter
  • the discrete channel seen at the output from the whitener filter may vary significantly from one timeslot to the next. This variation is due mainly to the change in propagation conditions between the transmitter and the receiver and to the frequency stability at the receiver.
  • Propagation conditions have a direct influence on the observed multipath channel. They change due to a modification in the environment or a displacement of the transmitter and/or the receiver. They create a time variation in the discrete channel, both between successive timeslots and within the same timeslot.
  • the variation of the discrete channel between two successive timeslots allocated to the same user is particularly large when the time interval between these timeslots is large. This variation is accentuated, even at a single timeslot, due to an increase in the carrier frequency or the speed of the transmitter and/or the receiver.
  • the variation of the discrete channel between two timeslots is sufficiently large to prevent any modulated estimate of the channel.
  • the estimate of the channel in a timeslot must then be based solely on the samples of the corresponding reference sequence.
  • this reference sequence provides an unbiased estimate of the discrete channel at the mid-point of the timeslot.
  • an invariable channel is usually assumed within a received timeslot. In this precise case, the estimate obtained at the mid-point of the frame can be used without degradation for equalization of the rest of the frame. But high speed movements of some terminals and the sustained demand for higher rate services operating at increasingly high radioelectric frequencies, make this assumption less and less justified.
  • the discrete channel may be affected by significant variations between the beginning and the end of a given timeslot. The difference between this real discrete channel and its estimate becomes increasingly large as the distance from the reference sequence increases. This may cause a large and irreversible deterioration in the reception quality and/or performances of the TDMA system.
  • the purpose of this invention is to overcome these disadvantages.
  • the purpose of this invention is to improve the performances of TDMA systems by reducing the ratio between the received power and the multiple access interference for a given reception quality, or in other terms, to improve the reception quality for a constant reception power.
  • This improvement in quality makes it possible to increase the capacity and coverage of TDMA systems such as GSM system, and particularly its EDGE extension to offer high rate services.
  • this improvement is obtained due to an optimization of the channel estimate at the receiver.
  • This optimization is a means of overcoming any deterioration in the performances generated by a fast variation in the channel between the beginning and the end of the same timeslot. It can also significantly reduce deterioration caused by an increase in the number of modulation states, without increasing the length or power of the reference sequence.
  • Another purpose of this invention is to reduce the cost price of terminals by making them less sensitive to the poor frequency stability of an inexpensive local oscillator (for the same reception quality), for example such that the received signal can be transposed into base band.
  • the invention can also reduce the number and/or power of reference symbols transmitted during each timeslot, for the same reception quality.
  • This purpose is achieved by taking account of data symbols in the discrete channel estimate that are usually more numerous than the reference symbols.
  • This purpose is also achieved by the optimum usage of samples corresponding to the reference symbols and/or data symbols of an arbitrary number of timeslots allocated to the user. This usage is achieved even in the case of large variations in the channel between two successive timeslots belonging to the same user.
  • this purpose is achieved by the optimum usage of samples from the common signal channel, and possibly users on the down link.
  • the reference symbols are distributed into groups throughout the duration of the allocated timeslot, which guarantees better tracking of the channel variation and therefore increased robustness with regard to high displacement speeds and poor frequency stability of the local oscillator.
  • Reference sequences may be chosen independently of each other, but they must always have good autocorrelation properties. They may be derived from short CAZAC type sequences.
  • the energy transmitted per symbol may vary from one symbol to another, without causing difficulties for the channel estimate which is always done optimally.
  • a timeslot is processed by block every time that the samples corresponding to this timeslot and possibly to other timeslots (originating from the same user, from other users or from the common signal channel) are available to make the channel estimate.
  • the first step is always a coarse estimate of the discrete channel using samples depending only on reference symbols only in the timeslot to be processed. This coarse estimate characterizes the phase and amplitude variation of all coefficients (improperly called “paths”) in the discrete channel selected for carrying out the equalization, for each reference or data symbol in the block to be processed, and symbol by symbol.
  • One of the characteristics of the invention is the use of a mesh to represent the multipath channel. This characteristic reduces the complexity of the receiver. If we consider the example of sequences of data symbols comprising n symbols without coding, with a two-state phase modulation (MDP2), each transmitted bit may be equal to either of two values. Since these two values are equally probable, this means that there are 2 n possible sequences of data symbols. Therefore the complexity of a traditional calculation using partial probabilities for all possible sequences increases exponentially (2 n ) with the number of symbols per sequence.
  • MDP2 two-state phase modulation
  • the labels of the branches of mesh sections change with the variation of the discrete channel with time in each of the timeslots forming the block.
  • an algorithm other than the Soft-Output Viterbi Algorithm (SOVA) [2] is used for a more precise characterization of the probabilities of the branches of the mesh dependent on the samples received. If the channel estimator is used optimally, these conditional probabilities may be determined using a BAHL or BCJR (abbreviation for Bahl Coke Jelinek Raviv) algorithm [6].
  • BAHL or BCJR abbreviation for Bahl Coke Jelinek Raviv
  • Other simpler algorithms [10] usually derived from linearization of this algorithm, may also be used, however performances will be slightly reduced. They can considerably reduce the complexity of the channel estimator.
  • the only weighted outputs provided by the SOVA algorithm are used directly after de-interlacing to decode the transmitted information.
  • conditional probabilities indirectly characterizing the data symbols are used in addition to the reference symbols to provide a better quality estimate of the discrete channel.
  • the improved estimate of the discrete channel obtained at the end of a given iteration may be used to improve the quality and reliability of conditional probabilities of branches of the mesh characterizing the discrete channel. These improved conditional probabilities may then be used jointly with the reference symbols to provide an additional improvement to the estimate of the discrete channel.
  • an iterative estimate will not give an optimum estimate of the discrete channel until after an infinite number of iterations has been carried out. However in practice, a few iterations are sufficient to obtain performances that are almost as good as an optimum estimate.
  • the corresponding mesh may be used either by the BAHL optimal algorithm (or by any simplification of it), or by the SOVA algorithm to provide improved weighted outputs to the decoder.
  • the optimum nature of the receiver according to the invention is related to the quality of the discrete channel estimate seen during a given timeslot. This optimum nature is based on the use of an iterative algorithm called the SAGE (Space-Alternating Generalized Expectation-Maximization Algorithm) [7] to find the most probable channel set up according to samples received from the block to be processed.
  • the SAGE algorithm is an extension of the EM (Expectation-Maximization) [8, 9] algorithm, that eliminates the problem of coupling between coefficients of the discrete channel while they are being estimated.
  • the estimate of the discrete channel is also based on the decomposition of each discrete channel path to be estimated according to a KARHUNEN-LOEVE [3] expansion algorithm.
  • This decomposition provides firstly a soft characterization of the variations with time of each of the discrete paths, and secondly is naturally integrated into the SAGE algorithm. It can also process cases in which the energy transmitted per symbol varies from one symbol to another.
  • the discrete channel estimate is based on the use of the BAHL algorithm which provides the probabilities of the mesh branches characterizing the discrete channel to each iteration of the SAGE algorithm, according to received samples and the channel estimate supplied in the previous iteration.
  • the purpose of the invention is a radiomobile communication process of the time division multiple access type, in which timeslots are allocated to several users for transmission and reception of radioelectric signals, and in which:
  • FIG. 1 already described, shows the distribution of timeslots allocated to several users
  • FIG. 2 is a diagram illustrating transmission and reception using the TDMA technique
  • FIG. 3 shows variations of the bit error rate (BER) as a function of the normalized Doppler spreading (B D T S );
  • FIG. 4 shows variations of the bit error rate (BER) as a function of the ⁇ S /No ratio for MDP4 and MDP8 modulations, in a first configuration and for a discrete channel with two paths;
  • BER bit error rate
  • FIG. 5 shows variations of the bit error rate (BER) as a function of the ⁇ S /No ratio for the MDP4 and MDP8 modulations in a second configuration with a discrete channel with two paths;
  • FIG. 6 shows variations of the bit error rate (BER) as a function of the ⁇ S /No ratio for an MDP4 modulation using the second configuration and a discrete channel with four paths;
  • FIG. 7 shows variations of the bit error rate (BER) as a function of the ⁇ S /N ratio for an MDP4 modulation using a discrete channel with one, two and four paths;
  • FIG. 8 is a view of the discrete channel seen at the output from the whitener filter, in the form of an offset register
  • FIG. 9 illustrates the estimate of the filter coefficients of the discrete channel by correlation of received samples with a CAZAC sequence and its circular offsets
  • FIG. 10 shows the distribution of the largest eigenvalues of the covariance matrix for three normalized Doppler spreadings
  • FIG. 11 illustrates a representation of the mesh of the normalized discrete channel seen at the output from the whitener filter for a channel with two paths and a modulation with two states and a length of the timeslot equal to four;
  • FIG. 12 shows the chronology of processing done on reception for a received timeslot
  • FIG. 13 shows the chronology of processing done in an elementary iteration of the channel estimating algorithm.
  • the performances of the process according to the invention have been compared with the performances of a variant of the conventional process used for the GMS system [1].
  • a conventional receiver in the GSM system starts by estimating the discrete channel at the mid-point of the timeslot to be processed by correlation of received samples that depend solely on the reference sequence with the corresponding CAZAC sequence. It then equalizes the other received samples using the SOVA algorithm in order to decode the transmitted information symbols.
  • the SOVA sub-optimal algorithm was replaced by the BAHL optimal algorithm used in the invention, in order to equitably evaluate the intrinsic improvement in performances provided by the invention compared with a conventional GSM receiver.
  • the comparison is made using the variation in the unmodified bit error rate (BER) (without considering any error correction or detection coding), for reference symbols grouped at the mid-point of the timeslot to be processed (like the GSM system), and distributed in small groups throughout the duration of this timeslot (according to the invention) in order to give better tracking of the variation of the channel with time.
  • BER bit error rate
  • FIG. 3 thus shows the variation of the BER as a function of the normalized Doppler spreading B D T S , which is the product of the Doppler spreading B D and the symbol duration T S that characterizes the variation intensity of the channel due to displacement of the transmitter and/or receiver.
  • Doppler spreading is proportional to the speed of the mobile terminal and to the carrier frequency. The frequency instability of the local oscillator, which is ignored here, introduces additional performance deteriorations.
  • the MDP4 modulation was selected (modulation with 4-state phase displacement).
  • the ⁇ S /M ratio between the average energy received per symbol and the noise level is 10 dB.
  • Three configurations were considered:
  • FIG. 3 shows representative curves corresponding to the following cases:
  • Table 1 contains figures characterizing the improved performances provided by the invention with regard to the improved conventional algorithm used in the GSM system.
  • C.R. means “conventional receiver” and I.R. means receiver according to the invention.
  • the ⁇ S /N o ratio between the average energy received per symbol and the noise level is 10 dB.
  • the improvement due to the invention is negligible in the case of a long central reference sequence (first configuration).
  • the reference sequence is sufficiently long to guarantee a good channel estimating quality, without the use of unknown data sequences.
  • the receiver according to the invention can give better performances than a conventional receiver, but also the performances are comparable to performances obtained with the long reference sequence of 26 reference symbols. Consequently, the receiver according to the invention is made insensitive to even a large reduction in the size of the reference sequence. This result is explained by the fact that the channel estimate makes use of symbols in data sequences that cooperate with reference symbols.
  • the receiver according to the invention is capable of keeping the bit error rate almost unchanged by varying the normalized Doppler spreading between 1/2500 and 1/100.
  • the selected modulations are MDP4 and MDP8 modulations.
  • the curves are applicable to the following cases:
  • the curves are applicable to the following cases:
  • the curves are applicable to the following cases:
  • the curves in FIGS. 4 and 5 show that, unlike a receiver according to the invention, the performances of a conventional receiver in the GSM system are very sensitive to the length of the reference sequence used and deteriorate significantly between the first configuration and the second configuration.
  • the curves in FIGS. 5 and 6 also show that performance deteriorations with a conventional receiver increase significantly with the number of paths although conversely these deteriorations remain almost unchanged and are low for a receiver according to the invention. Therefore, the receiver according to the invention has excellent robustness with respect to any reduction in the length of the reference sequence and any increase in the number of channel paths.
  • Table 2 contains figures characterizing the improvement in performances provided by the receiver according to the invention compared with the improved GSM system algorithm, for the MDP4 modulation.
  • This table shows that a receiver according to the invention always has better performances than an improved conventional receiver, for a given length (first or second configuration) of the reference sequence. These results also show that the improvement provided by the invention is particularly significant when the length of the reference sequence is short or when the number of paths in the channel is increased. These results also show that even with a short reference sequence (second configuration), a receiver according to the invention always has better performances than a conventional receiver with a long reference sequence (first configuration).
  • the MDP4 modulation is always selected.
  • a single configuration with three distributed reference sequences is considered. Each sequence is composed of 4+L ⁇ 1 bipolar symbols and is obtained by cyclic extension (expect for a sign and an offset) of the single bipolar CAZAC sequence with length 4 , namely ⁇ 1, +1, +1, +1.
  • Doppler spreading considered is sufficiently severe so that a conventional receiver cannot follow the variations of each path of the discrete channel that may be affected by phase rotations equal to ⁇ between the beginning and end of each timeslot.
  • a receiver determines the production of the most probable discrete channel during a given timeslot, depending on the samples received from the block to be processed. This determination is made using a Maximum A Posteriori (MAP) probability criterion. This channel estimate requires knowledge of a priori probabilities of symbols in transmitted data sequences.
  • MAP Maximum A Posteriori
  • each block to be processed for the channel estimate is composed solely of received samples related to a single timeslot.
  • symbols reference or other symbols
  • the transposition operator is denoted (.)′.
  • the transmitted energy E k associated with each symbol a k is independent of values taken on by this symbol but it may vary from one symbol in the timeslot to another.
  • FIG. 8 a shows all means between the input to the transmitter modulator and the output from the receiver whitener filtering. Therefore this figure shows a view of the real radioelectric channel and the processing done in the receiver (demodulation, matched filtering and whitening filter). This figure shows the modulator 91 , a block 92 symbolizing the multi-path channel, the demodulator 93 with its matched filter 94 and its whitener filter 95 .
  • FIG. 8 b shows a view of these means in the form of an offset register with (L ⁇ 1) cells Y 1 , Y 2 , . . . , Y L ⁇ 1 .
  • This register receives the current symbol a n and the cells contain the symbols with a delay of one symbol period namely a n ⁇ 1 , a n ⁇ 2 , . . . , a n ⁇ (L ⁇ 1) .
  • the circuit shown also comprises (L) multipliers Z 0 , Z 1 , . . . , Z L ⁇ 1 that contain (L) coefficients C n 0 , C n 1 , . . . C n L ⁇ 1 respectively, an adder S connected to the multipliers, and a final adder receiving a signal w n representing a noise. This final adder outputs a signal r n .
  • the coefficients c k 1 for the discrete channel satisfying k ⁇ 1 or k>N+1 are used in the expression of R k although they are equal to zero.
  • the transmitted symbols a k satisfying k ⁇ 0 or k>N ⁇ 1 appear in this expression of R k although they are equal to zero.
  • Doppler power spectra usually encountered in radiomobile communications are either conventional (in external environments) or flat (in internal environments).
  • the average power ⁇ 0 1 varies from one path to another and characterizes the multipath intensity profile [3] of the discrete channel.
  • MAP maximum a posteriori
  • the vectors of the orthonormal base associated with the l th path are simply the eigenvectors of the co-variance matrix H′ of the normalized vector C′ associated with this path.
  • the receiver according to the invention must normally have L orthonormal bases associated with each of the L paths in the discrete channel in order to rebuild or decompose any intermediate or final estimate of the discrete channel.
  • the receiver In order to generate the orthonormal base for the l th path, the receiver must have the most precise possible estimate of the co-variance matrix H′ for this path. Consequently, it must have the most precise possible knowledge of the characteristics of the Doppler power spectrum of the radioelectric channel. This knowledge is regularly updated and must include an estimate of Doppler spreading B D , or an upper limit to it. It may possibly comprise an estimate of the average power of each path in the discrete channel and the shape of the Doppler power spectrum. Depending on this knowledge, the receiver may either calculate appropriate orthonormal bases in real time, or search in a bank of pre-calculated orthonormal bases for the bases that best match the characteristics of the real channel.
  • the receiver does not have precise knowledge of the shape of the Doppler power spectrum, or perfect and instantaneous knowledge of Doppler spreading. In this typical case, it may be assumed that the Doppler power spectrum is flat, and that the real Doppler spreading is equal to the upper limit of Doppler spreading. Furthermore, the receiver does not need to have a precise estimate of the average power of each of the discrete channel paths taken individually. Also in this case, a discrete channel with L paths with equal average powers may be assumed.
  • the estimate of the c′ vectors characterizing the L discrete channel paths is made iteratively using the MAP criterion through the normalized vectors C′ or their appropriate representation G′. This estimate may take optimal account both of the characteristics of the data symbols and the transmitted reference symbols (statistics and energy) and the characteristics of the multi-path channel.
  • R ) , which maximizes the conditional a posteriori probability density p( ⁇ G 1 ⁇ l 0 L ⁇ 1
  • a solution as close as necessary to the exact solution can be obtained by iteration using the SAGE extension [7] of the EM algorithm [8, 9].
  • conditional a posteriori probability density p( ⁇ G 1 ⁇ l 1 L ⁇ 1
  • one or several reference sequences are necessary each having good autocorrelation properties. Like the GSM system, these sequences may be built starting from CAZAC sequences by extension or circular swapping. These sequences are composed of symbols with a constant modulus and with a zero circular autocorrelation function everywhere except at the origin.
  • CAZAC sequences with symbols belonging to modulation constellation used to transfer data symbols.
  • the shortest CAZAC sequence alone except for a sign and a circular swap
  • the shortest CAZAC sequence alone has four symbols.
  • the shortest CAZAC sequence alone using the ⁇ l, i, ⁇ l, i ⁇ constellation, the shortest CAZAC sequence alone (still with a multiplication factor i, ⁇ 1 or ⁇ i, and except for a circular offset), namely ⁇ l,i ⁇ is composed of only 2 symbols.
  • a reference sequence based on a CAZAC sequence with length M can only estimate up to M paths of the discrete channel. It is obtained by cyclic extension of L ⁇ 1 positions of this CAZAC sequence and contains a total of M+L ⁇ 1 symbols. Therefore the length M of the CAZAC sequence needs to be greater than or equal to the number of paths L of the discrete channel to be estimated.
  • it is sometimes desirable to use short CAZAC sequences for a small number of paths L to be estimated (less than or equal to 4 for an MDP2 modulation and 2 for MDP4, MDP8 modulations, etc.), since they can significantly reduce the total number of reference symbols per timeslot, while guaranteeing more regular and more frequent sampling of the discrete channel, particularly in an environment with large Doppler spreading.
  • the first line A gives the reference sequence
  • the second line T 1 corresponds to the first path
  • the third line T 2 corresponds to the second path
  • the fourth line S gives the composition of the received samples.
  • the elementary reference sequence occupies positions between n ⁇ 4 and n in the timeslot to be processed.
  • R n C n 0 A n +C n 1 A n ⁇ 1 +W n ⁇ 1 +W n ⁇ 1
  • R n C n 0 A n +C n 1 A n ⁇ 1 +W n ⁇ 1 +W n ⁇ 1
  • R n C n 0 A
  • the coarse estimate of the L channel coefficients at a given instant in the timeslot is obtained by correlation of samples that depend solely on the reference sequence with L offset versions of the corresponding CAZAC sequence.
  • Each reference sequence built up by circular extension of a CAZAC sequence can be used to obtain a noisy sample of each of the discrete channel paths.
  • the number of samples per timeslot necessary for reconstruction of the channel depends on the normalized Doppler spreading B D T S and the number N of symbols making up this timeslot. As the product B D T S N increases, the variation in the channel from one end of the timeslot to the other increases, and the number of elementary reference sequences needs to be greater.
  • An elementary reference sequence is a sub-set of grouped symbols in the reference sequence associated with the timeslot obtained starting from a circular extension of a CAZAC sequence.
  • the two eigenvectors associated with the two largest eigenvalues are necessary for a precise reconstruction of the discrete channel. These two vectors vary sufficiently so that a reference sequence composed of two elementary sequences located on each side of the mid-point of the timeslot are necessary.
  • K be the number of elementary reference sequences per timeslot to be processed.
  • the weighting factor W k d depends on the normal N k 1 of the restriction of eigenvectors to include only samples corresponding directly to channel samples procured by the reference sequence. It also depends on the quality of the contribution of the eigenvector B 1k measured by the ⁇ 1k /N 0 ratio. As the variance ⁇ 1k of the coefficient G k 1 in the representation of the discrete channel increases in comparison with the variance N 0 of noise samples, the corresponding weighting also increases and approaches 1.
  • the k th component of the (d+1) th re-estimate G 1(d+1) of the G 1 vector associated with the l th path is obtained using the expression:
  • the weightings w k 1 take account of the quality of the contribution of the vector B 1k to the appropriate representation of the discrete channel.
  • a n is transmitted, which is why it is useful to weight this expression later by the conditional a posteriori probability P(A n
  • conditional probabilities may be calculated precisely using the BAHL algorithm, also known as the BCJR algorithm [6]. They may also be calculated approximately and easily using linearized variants of the BAHL algorithm [10].
  • the following describes an outline of the calculation of the conditional probabilities P(A n
  • the sample R n obtained at instant n depends on the symbol A n transmitted at this instant and the L ⁇ 1 symbols A n ⁇ 1 , A n ⁇ 2 , . . . , A n ⁇ (L ⁇ 1) preceding it.
  • the modulator—multi-path channel—demodulator assembly may be modeled using a MARKOV discrete time sequence.
  • This type of mesh represents the expected output from the channel as a function of time and depending on the transmitted symbols.
  • This expression shows that information about the past may be acquired either through probabilities associated with the instant immediately preceding the current instant or through the probabilities of transitions of the mesh branches.
  • a priori probabilities may characterize a possible coding of the actually transmitted modulated symbols. They may also characterize the reference symbols that are known to the receiver and that have only one possible value. For these reference symbols, the a priori probability P(A n ) is equal to 1 for the value actually transmitted and 0 for other possible values of the modulation.
  • BAHL algorithm is fairly complex and that in practice it is better to use approximate algorithms that can significantly reduce the complexity of the calculations without excessively reducing performances.
  • the use of these approximate algorithms is recommended particularly when the number of paths and/or modulation states is high.
  • the VITERBI algorithm searches for the most probable transmitted sequence. Therefore, it can reduce the probability of decision errors on these transmitted sequences.
  • the SOVA algorithm is a VITERBI algorithm with weighted outputs. It enables a more precise characterization of the reliability of decisions made with the VITERBI algorithm.
  • the BAHL algorithm can determine the a posteriori probability density for each transmitted symbol, depending on the received samples and the obtained channel estimate. Therefore, it can determine the most probable value of each transmitted symbol and therefore reduce the error rate. Weighted outputs are obtained through symbol probabilities depending on received samples.
  • weighted outputs are only useful if corrector decoding or source coding with weighed inputs is used in order to increase the receiver performances.
  • R * ⁇ ⁇ G l ⁇ ⁇ ( D ) ⁇ l 0 L - 1 )
  • Firm or soft decisions on the transmitted symbols are supplied to an error corrector decoder or a source decoder by means 123 that may use the VITERBI algorithm [3], the SOVA algorithm [2], the BAHL algorithm [6] or the linearized BAHL algorithm [10].
  • FIG. 13 illustrates the L steps making up each iteration and that are necessary for successive estimate of each of the L paths.
  • the (d+1) th iteration d+1 of the channel estimator uses the means 121 and 122 shown in FIG.
  • the (d+1) th iteration executes a third step, once again based on the BAHL algorithm and represented by the BAHL block, reference 132 to produce conditional a posteriori probabilities P(A n
  • the (d+1) th iteration executes a fourth step based on the SAGE algorithm and shown by the SAGE 1 block reference 133 , to enable the (d+1) th re-estimate G 1(d+1) of the 1 th path.
  • the (d+1) th iteration executes a final step based on the BAHL algorithm and represented by the BAHL l ⁇ 1 block reference 134 , to output conditional a posteriori probabilities P(A n
  • R * ⁇ G m(d+1) ⁇ m 0 * L ⁇ 1 , ⁇ G (L ⁇ 1),(d) ⁇ ) starting from the d th re-estimate of the last channel path and the (d+1) th re-estimate of the first L ⁇ 1 paths of this channel.
  • the (d+1) th iteration then executes a final step, based on the SAGE algorithm and represented by the SAGE L ⁇ 1 block reference 135 , to make the (d+1) th re-estimate G (L ⁇ 1),(d ⁇ 1) of the L th path.
  • the first iteration symbolized by block 0 reference 1201 in FIG. 12 cannot use the BAHL and SAGE algorithms to calculate the first estimate of the discrete channel.
  • the reference symbols for which a priori and a posteriori probabilities are well known to the receiver are used to make this first estimate.

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Power Engineering (AREA)
  • Noise Elimination (AREA)
  • Time-Division Multiplex Systems (AREA)
  • Cable Transmission Systems, Equalization Of Radio And Reduction Of Echo (AREA)
  • Digital Transmission Methods That Use Modulated Carrier Waves (AREA)
  • Mobile Radio Communication Systems (AREA)
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US8463188B2 (en) * 2009-01-06 2013-06-11 Huawei Technologies Co., Ltd. Method and apparatus for spectrum access of secondary users in cognitive radio system
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US20130114766A1 (en) * 2010-07-30 2013-05-09 Telefonaktiebolaget L M Ericsson (Publ) Decoding Technique for Tail-Biting Codes
US8995583B2 (en) * 2010-07-30 2015-03-31 Telefonaktiebolaget L M Ericsson (Publ) Decoding technique for tail-biting codes
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JP4472904B2 (ja) 2010-06-02
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EP1180289A1 (fr) 2002-02-20
FR2794589A1 (fr) 2000-12-08
FR2794589B1 (fr) 2001-08-24

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